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  • Arithmetic
    • The True Fundamentals >
      • The Language of Mathematics >
        • The Importance of Definitions >
          • Keeping consistent language
          • Defining "definition"
          • The world of mathematical definitions
        • Understanding the Basics of Axioms, Theorems, and Proofs >
          • Axioms
          • Theorems
          • Proofs
        • Inverses and Their Implications >
          • A brief mathematical interlude
          • Understanding inverses
          • Mathematical operations and inverses
        • Simplifying in Mathematics and Life
        • Theoretical versus Applied Mathematics
    • Part 2 | Sets and Numbers >
      • Chapter 1 | Sets of Objects
      • Chapter 2 | Sets of Numbers
      • Chapter 3 | Operations on Numbers
  • Algebra
    • Part 1 | Adjusting to Algebra >
      • Chapter 1 | An Introduction to Algebra >
        • Section 1.7 | Solving Algebraic Equations in One Variable
    • Part 2 | Developmental Linear Algebra >
      • Preface
      • Chapter 1 | Linear Equations in One Variable and Their Applications >
        • Section 1.3 | Applications Involving Solutions of Linear Equations in One Variable: Percent
      • Chapter 2 | Linear Equations in Two Variables and Their Applications
      • Chapter 3 | Systems of Linear Equations
      • Chapter 4 | Linear Inequalities, Systems of Linear Inequalities, and Their Applications >
        • Section 4.2 | Solving Absolute Value Equations and Inequalities
    • Part 3 | Functions >
      • Chapter 1 | Functions
      • Chapter 2 | Connecting Concepts - From Linear Equations to Linear Functions
    • Part 4 | Exponential Algebra >
      • Chapter 1 | Exponents
      • Chapter 2 | Radical Expressions and Equations >
        • Radicals and Roots
      • Chapter 3 | Exponential and Logarithmic Functions >
        • Exponentials and Logarithms
    • Part 5 | Polynomial Algebra >
      • Chapter 1 | Introduction to Polynomials and Polynomial Functions
      • Chapter 2 | Factoring Polynomials
      • Chapter 3 | Solving Polynomial Equations
      • Chapter 4 | Applications and Graphing Quadratic and Polynomial Functions >
        • Section 4.11: Solving Polynomial Inequalities
        • Quadratics
      • Chapter 5 | Conic Sections >
        • Section 5.1 | An Introduction to Conic Sections
        • Section 5.2 | Parabolas Revisited
        • Section 5.3 | Ellipses
        • Section 5.4 | Hyperbolas
    • Part 6 | Rational Algebra >
      • Chapter 1 | Ratios of Polynomials >
        • Rationals
        • Section 1.7: Problem Solving Using Rational Equations
        • Section 1.8: Inverse, Joint, and Combined Variation
  • Calculus
    • Part 1 | Limits >
      • The Collection of Limit Proofs
    • Part 2 | Total Derivatives >
      • The Collection of Derivative Proofs
    • Part 3 | Single Integrals >
      • Chapter 2 | Techniques of Integration >
        • Section 2.7 | Basic Numerical Integration >
          • 2.7.1 | What is numerical integration?
          • 2.7.2 | An overview of basic numerical integration techniques
          • 2.7.3 | Integrating numerically
        • Section 2.9 | Improper Integrals
        • Section 2.10 | The Integral Comparison Theorem
        • Section 2.11 | A Summary of Integration Techniques
      • Chapter 3 | Applications of Integration >
        • Section 3.2 | Fluid Pressure
        • Section 3.3 | Center of Mass
        • Section 3.4 | Average Value of a Function
        • Section 3.5 | Lengths of Curves
        • Section 3.6 | Surface Area of Revolved Objects
      • Chapter 4 | The Calculus of Parametric Curves >
        • Section 4.1 | Derivatives of Parametric Curves
        • Section 4.2 | Areas Defined by Parametric Curves
        • Section 4.3 | Curve Lengths and Surface Areas of Parametric Curves
    • Part 4 | Infinite Sequences and Series >
      • Chapter 1 | Convergence and Divergence of Series
      • Chapter 2 | Power Series >
        • Theorem and Proof | Taylor's Inequality
    • Part 5 | Partial Derivatives
    • Part 6 | Multiple Integrals
    • Part 7 | Vectors and Vector Calculus
  • Differential Equations
    • The Basics of Differential Equations >
      • Lecture 1 The Language of Differential Equations
      • Lecture 2 An Introduction to Solutions of Differential Equations
    • Laplace Transforms
    • Final Exam Review >
      • First-Order ODEs
      • Higher-Order ODEs
  • Calculators
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    • Calculus
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        • Factoring Example Level 6
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